Velocity estimation by coherency inversion provides a velocity-depth macro-model of the subsurface. The accuracy of this model is critical for imaging techniques such as depth migration and inversion. Therefore, the reliability of seismic interpretation is strongly dependent on the accuracy of the derived model. Uncertainties in the velocity and depth estimates for the model can be calculated using a combination of the response surface technique and the Dix equation. In the layer-stripping strategy, the method takes into account the local errors connected mainly to the current layer and the global errors connected to the derived overburden. Examples using synthetic and real data show that the coherency inversion produces accurate macro-models.
One of the main challenges of 3-D reflection seismology is providing the spatial sampling required to avoid aliasing. In practice, fine-scale and regular acquisition geometry is possible only in 2-D seismic surveys. 3-D surveys typically have sparse and irregular geometry that often results in spatial aliasing. In this paper we present a processing method to overcome this problem that is suitable for sparse and irregular acquisition geometry, and yields better results than does conventional processing such as dip moveout.The objective of the process is to obtain the hypothetical data that would be recorded in an adequately sampled zero-offset experiment, that best fits the data with a given velocity model. The process takes advantage of what seems to be redundancy in multifold seismic data, to overcome spatial aliasing which is a missing data problem.Our computer implementation involves pre-processing of gain, normal moveout removal, log-stretch transform and Fourier transform. After the log stretching, the relation between the data and the model is time invariant, making inversion practical in the space-frequency (X-F) domain, using a linear inversion, frequency by frequency. After the inversion, the data are inverse-Fourier and inverse-log transformed. The result is ready for post-stack migration.
Velocity estimation is examined in 3-D layered structures formed by plane and curved interfaces. The applied technique of coherency inversion tests the layer velocity through the repeating sequence of ray migration/coherency measurement. The reconstructed velocity‐depth model fits zero‐offset reflection times and maximizes semblance on input common midpoint (CMP) gathers. The correctness of layer velocity analysis disregarding the three‐dimensionality of the structures is under consideration. Using the 2-D coherency inversion technique, velocity is correctly determined in the upper layer of the examined structures. Two‐dimensional analysis in the deeper layer gives biased velocity estimates. The errors in the 2-D velocity estimates vary with the profile azimuth and appear in the form of the apparent velocity anisotropy. The inaccuracy of 2-D velocity estimation is analytically considered for the profile oriented along the refractor strike direction. The derived equation relates the velocity error to structure geometry and to the velocity contrast above and below the refractor. Three‐dimensional velocity analysis in the examined structures reveals that the layer velocity resolution is affected by the refractor shape. Below the convex refractor the velocity resolution deteriorates compared with that below the plane.
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